Every cell, whether it is of type Math, Text, or Input, can use the special variables row and col. Row 1 is the first non-header row and column 1 is the first non-header column. This implies that the top header in the image above has a row index of 0. If there are multiple headers, the row index will be negative.

You can refer to the content of a Math cell or an Input cell through the cell function, which takes the row index and column index as arguments respectively.

The example above shows a table corresponding to the Fibonacci sequence.

Relations and free input

A powerful feature of these relations is that the values of the cells do not to be known in advance. You can create a Math Table where a student is free to choose some values. Consider the example below, where the student has to create a table for a given function. The student is free to choose the values for x, while the relations enforce that these x-values are increasing and that the values for y are correct.

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This example illustrates a situation where you want to specify a condition on the table. The student is required to try different divisors of -30, until a pair is found that sums to -13.

The Input cells in columns 2 and 3 are of type Math Entry and allow any integer divisor of -30. The Input cells in the last column are of type Algebra with the task to sum the two divisors.

The student has successfully finished the table when the correct divisors are found, which are -15 and 2. It doesn’t matter in which row these divisors are written or in which order the divisors are given, as long as they exist. This requires a condition like “There exists a cell in the last column with value -13”.

Such a condition can be created under the Table tab:

• Check the ‘Existence’ check box to indicate that the condition is valid if a cell can be found that satisfies it. If this checkbox is not checked, then all cells need to satisfy the condition.
• Click the button ‘change…’ to select the range of cells that apply to this condition. In our case, these are the cells in the last column
• Enter the condition in the formula box. The variables r1 and c1 are the row and column index of the cell that meets the condition (if any).
• Specify that the problem is finished if a cell is found that matches this condition. Specify feedback in case it is not found.

Note that the student input is evaluated as correct only if all the conditions in the cells and the table condition are satisfied. So just entering the number -13 in the last column is not a valid answer.

In the General settings, you can set the tolerance and define whether you want to hide the Toolbar. This last option is particularly useful in case you want to use the number line as a resource/image rather than as an interactive component.

The tolerance defines the error margin a student has for drawing the elements on the number line. The values you can enter are either decimal values (decimal point separated) or integer values.

The values correspond with the scale of the number line. That is, if your number line ranges from 0 to 10, and you set the tolerance to 1, a student is allowed to enter a point between 5 and 7 for the point at coordinate 6.

The Boundaries settings are used to define the lowest and highest value of the number line.

With the following settings:

The number line would look like this (starting at 0, ending at 10):

For more detailed settings on the ticks, refer to the Ticks settings below.

The Guide Lines setting is available to define the amount of guidelines on which number line elements can be created. You can create multiple guidelines to prevent overlap of intervals. Note that only the horizontal position of an element is taken into account for evaluation. Increasing the number of guide lines is merely a visual enhancement to create a more clear number line.

With an amount of 3 number lines, you can create a setting such as:

The Regular Ticks settings control the regular step markings of the number line, commonly named ticks. These are split between major ticks, longer markings that can display their axis value, and minor ticks, shorter markings to indicate smaller increments.

The step size between major ticks is controlled using the Major Step field. The number of minor ticks per major step are indicated with the Minor Divisions input field.

Labels of major ticks can be disabled to only show the step markings. Moreover, the regular ticks can be disabled altogether, resulting in a blank horizontal axis for displaying Custom Ticks (see below) only.

For example:

Will result in a number line with 1 subdivision per major step, and the major steps labelled per integer:

Custom Ticks are disabled by default, but can be enabled to define your own marked positions. The Positions list can be extended number-by-number to provide an array of irregular ticks to occupy the number line axis. The values entered should be integer or decimal values, written with a decimal point if applicable.

Note that custom ticks can be used in tandem with regular ticks to highlight specific values.

For example:

Will result in two custom ticks below the number line:

The first block on the page contains a lot of information that is one-off. Therefore, it is now collapsed by default.

• The name of the exercise (text input) and the audience (dropdown select) remain directly available for change. These are the first two items in the row visible.

• The exercise-ID is not directly visible anymore, but available via the clipboard copy button at the end of the row.

• The remaining options are available via the available tabs (when they were set in the exercise before).

• If a tab is not listed, you can add it by clicking the settings button in front of the row, and selecting the name of the tab you want to access.

• The general settings and metadata are now available via the settings tab, rather than directly visible upon opening the exercise.

The interaction settings are now available via the interaction dropdown menu rather than directly visible at each interaction. By clicking the arrow next to the interaction name, you can access the settings.

• Hints opens the context hints item as before, but is now called hints, rather than context hints.

The step settings are now not available for selection anymore, as they have been deprecated and replaced by new functionality. In case you want to use a different evaluation method or want to describe specific answers, the interaction type Math Entry is recommended.

The Actions dropdown button lists all the step settings which are available, such as accuracy, units, alternative answers, etc.

The expression in a Math cell has to be valid mathematics so that AlgebraKiT is able to interpret it. This allows you to define relations that refer to math cells, as you will see when we discuss table relations.

If the simplify expression checkbox is enabled, AlgebraKiT will evaluate and simplify the expression before it is displayed to the student. This feature is convenient if the math expression refers to randomized script variables.

A Text cell contains general content, such as text, images, and mathematical expressions. These cells are for display only, so it is not possible to use them in relations. The upside of this is that you can embed any mathematical expression, even invalid mathematics like y=....
Such an expression would not be allowed in the Math cell.

The Input cell hosts an interaction of the type Algebra or Math Entry. The student will see a math input box where a mathematical expression can be entered. Refer to Algebra Interaction or Math Entry Interaction for more information about these interaction types.